WASHINGTON – The guilty plea by Donald Trump's former lawyer to campaign finance violations and other charges raises serious questions about the president's behavior, a majority of Americans say in a USA TODAY/Suffolk University Poll.

Nearly two-thirds say the president should agree to be interviewed by special counsel Robert Mueller.

Those surveyed express significantly higher levels of trust in Mueller's rectitude than in Trump's denials that his campaign colluded with Russia to interfere in the 2016 election. The poll of 1,000 registered voters was taken Thursday through Tuesday, after former Trump lawyer Michael Cohen pleaded guilty to violating campaign finance law and other charges and former Trump campaign chairman Paul Manafort was convicted of tax evasion and financial crimes.

The findings underscore the perils for the president as the special counsel moves from an investigation that has been conducted largely behind closed doors to one playing out in the drama of the courtroom.

"It's ludicrous that Trump continues to write the tweets that question Mueller's integrity," says Richard Dean, 71, a political independent. The retired engineer from Gadsden, Alabama, was among those called in the poll.

"From everything I've read, they've proven that there were certainly Russian meddling and hacking and hacking attempts, and why Trump won't admit that is ridiculous," Dean says. "In my mind, I suspect and I think they're about to prove that there was certainly collusion."

President Donald Trump has shown his disdain for special counsel Robert Mueller's investigation into Russian election meddling.(Photo: AFP/Getty Images)

Fifty-five percent say they have a lot or some trust in Mueller's investigation to be fair and accurate. Thirty-five percent say they have a lot or some trust in Trump's denials of collusion. The telephone survey has a margin of error of +/-3 percentage points.

Mueller, a longtime Republican who led the FBI under Presidents George W. Bush and Barack Obama, was appointed in May 2017 by the Justice Department to lead the Russia inquiry after Trump fired FBI Director James Comey. Trump has denied wrongdoing and labeled the inquiry a "witch hunt."

Approval rating slips, but not with party faithful

The president's approval rating edged down to 40 percent, 3 points lower than in the USA TODAY/Suffolk survey taken in June. He retains the approval of a solid 89 percent of Republican and Republican-leaning voters. Fifty-six percent overall disapprove of the job he is doing as president.

Gregory Bailey, 58, dispatcher and driver for an auto parts company in Oklahoma City, is among the Republican faithful, calling Mueller "corrupt" and his inquiry "a farce." He echoes some of the arguments Trump has made on Twitter against the investigation. Mueller "only hired Democrats for the investigation," Bailey says. "It doesn't take a year and a half to find something on Russian collusion, and collusion is not even a crime."

Most Americans are prepared to be patient: 55 percent say the special counsel should take all the time he needs to finish the investigation, even if it continues into next year; 40 percent say he should wrap it up within weeks, as Trump lawyer Rudy Giuliani has argued.

By 63 percent to 27 percent, those polled say Trump should agree to be interviewed by Mueller. That includes nearly a third of Republicans.

Nation split on question of impeachment

The nation is split on whether the House of Representatives should consider impeaching the president, based on what the voters know: 44 percent say yes, 47 percent say no.

"The man stood up in front of the entire world and said to the Russian government, to Putin, that he should look into Hillary Clinton's email," says Bonni Davis, 61, an attorney from New York City who is a Democrat. At a campaign news conference July 27, 2016, Trump encouraged "Russia, if you're listening," to try to find missing Clinton emails; an indictment released last month by the special counsel reported that Russian officials began to target Clinton-related email accounts "on or around" that same day.

In Davis' view, there is enough evidence for Congress to act. "That was beyond disgraceful," she says. "The fact that Russia meddled is beyond question. The fact that Trump supported Putin is beyond question, and that's not appropriate behavior for a president." She calls his actions "a threat to our democracy."

Carol Schmock, 63, a Republican and retired customer service representative from Auberry, California, sees more wrongdoing by former President Barack Obama and Democratic presidential nominee Clinton than by Trump, an allegation the president repeatedly has made.

"He hasn't done anything worth impeachment," she says. "He's actually a very good president." She ticks off his initiatives on immigration, North Korea and veterans' affairs. "It's just like he's magic, in a way."

There is, predictably, a sharp partisan divide on the question of impeachment. Even so, 9% of Republicans say the House should consider impeaching the president, and 18% of Democrats say it shouldn't. Among independents, 47% support impeachment; 40% oppose.

Some take a wait-and-see attitude.

"Mueller needs to finish his investigation, and whatever he finds, the public should be made aware and then make the decision from there," says Keith Walker, 59, a political independent and retired educator from Dover, Delaware.

"For me, it would take actually being shown that he did a crime, especially on the Russian part of it," says Melinda Strain, 50, a Democrat from Harrisburg, Missouri. "Morally, I think he's done a bunch of things that are wrong, but they aren't necessarily illegal."

What about the swamp?

Fewer than one in four of those surveyed, 23 percent, say Trump has delivered on his campaign promise to "drain the swamp" in Washington. A 57 percent majority, including nearly one in five Republicans, say "the swamp" has gotten worse during his administration.

The Manafort and Cohen cases reinforce the dyspeptic view of some toward the ethics of Washington in general and the president in particular.

"It's solid evidence of the person he is and the people he's surrounded himself with," says Benjamin Jones, 21, an independent who works in retail sales in Queens, New York. "This is real evidence that he is scandalous."

The turmoil over the Russia investigation may help explain a disparity in Americans' attitudes about the state of the nation. While nearly six in 10 say the economy is in a recovery, only one-third say the country is headed in the right direction.